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Lagrangian empirical design of variable-rate vector quantizers: consistency and convergence rates

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1 Author(s)
T. Linder ; Dept. of Math. & Stat., Queen's Univ., Kingston, Ont., Canada

The Lagrangian formulation of variable-rate vector quantization is known to yield useful necessary conditions for quantizer optimality and generalized Lloyd algorithms for quantizer design. The Lagrangian formulation is demonstrated to provide a convenient framework for analyzing the empirical design of variable-rate vector quantizers. In particular, the consistency of empirical design based on minimizing the Lagrangian performance over a stationary and ergodic training sequence is shown for sources with finite second moment. The finite sample performance is also studied for independent training data and sources with bounded support

Published in:

IEEE Transactions on Information Theory  (Volume:48 ,  Issue: 11 )